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Triangle equations are a staple of geometry and algebra courses, and the symbol X is most often used to denote an unknown angle. By analyzing the markings on the triangle and applying the fundamental property that the three interior angles sum to 180°, you can solve for X in any triangle—whether it’s right, isosceles, equilateral, acute, or obtuse. Graphing the triangle can also clarify the relationships between the angles and make the calculations more intuitive.

Determine the Type of Triangle

Inspect the figure for distinctive marks. A small square at an angle indicates a right triangle, where that corner is 90°.

If two base angles each have a half‑circle with a line through them, the triangle is isosceles; those two angles are congruent.

When all three angles display identical half‑circles with lines, the triangle is equilateral, and every angle is 60°.

Solving for X in a Right Triangle

Because a right triangle contains a 90° angle, the remaining two angles must add up to 90°. To find the unknown angle X, subtract the known angle(s) from 180°:

• If you know one acute angle, add it to the 90° right angle, then subtract that sum from 180° to get X.
• Alternatively, simply subtract the sum of the two known angles from 180°; the remainder is X.

Solving for X in an Isosceles Triangle

Because the two base angles are equal, the solution depends on which angles are provided:

• Base angles known: Double the given base angle value and subtract it from 180°. The result is the vertex angle X.
• Vertex angle known: Subtract the vertex angle from 180°, then divide the difference by two. The quotient is each base angle X.

Solving for X in Other Triangles

For acute or obtuse triangles, add the two given angles and subtract the sum from 180° to determine X. Verify the result against the triangle’s nature:

• If the triangle is obtuse, X must be greater than 90°.
• If the triangle is acute, X must be less than 90°.

In an equilateral triangle—identified by equal half‑circles at all three angles—each interior angle is automatically 60°, so X = 60° without further calculation.

References

• Teachers' Choice: Solving Triangles